The Markov Chain Simulator is an interactive and data-driven tool designed to help analysts, researchers, and decision-makers simulate and analyze the behavior of Markov processes. This tool allows users to define a transition matrix and initial state probabilities to simulate state transitions over time. It provides actionable insights into long-term steady-state probabilities, expected hitting times, and state trajectories, helping stakeholders make informed decisions in fields such as finance, biology, and operations research.

Key Features:

1. Dynamic Input Fields: Users can input a transition matrix and initial state probabilities for up to five states.
2. Simulation: Automatically simulate state transitions over a specified number of steps or until convergence to steady-state probabilities.
3. Interactive Charts: Visualize state trajectories, transition probabilities, and steady-state distributions using bar charts or line graphs for enhanced clarity.
4. Scenario Testing: Allow users to adjust inputs dynamically to explore how changes in the transition matrix affect outcomes.
5. PDF Export Functionality: Generate downloadable reports summarizing simulation results for presentations or sharing with stakeholders.
6. Modern and Stylish Design: A sleek interface with vibrant colors, animations, and clear typography to enhance user engagement.
7. Fully Responsive: Optimized for all devices, ensuring seamless functionality on desktops, tablets, and mobiles.
8. Self-Contained Container: The tool operates within its own container, ensuring no interference with the page header or footer.

Use Cases:

• Researchers modeling biological systems or population dynamics.
• Financial analysts simulating credit rating transitions or stock market regimes.
• Operations managers analyzing equipment reliability or customer journey flows.

How It Works:
Users input a transition matrix and initial state probabilities for up to five states. The tool simulates state transitions over a specified number of steps or until convergence to steady-state probabilities. Results are displayed in tables and visualizations, allowing users to interpret the behavior of the Markov chain. Users can customize inputs dynamically, analyze scenarios, and download detailed reports in PDF format for further analysis or sharing with stakeholders.